YummyMummy66:
It could be becasue this little guy is a puppy and heck, aren't all puppies cute?

MIL may realize that she is not getting any grandchildren from her son, (don't know if there are any other children, siblings).

Like others, I am not sure why this is such a big deal? Because she doesn't say the same thing about the other animals?

What I would do, is say, for her birthday or next holiday, (Easter is coming up if you celebrate that), get her a small basket with a card and sign all pet's names, something to a grandmother from her grandchildren. Or vice versa for a birthday card, from her "grandchildren".

My MIL loves her furbabies or girls as she calls them, (two cats), and for all birthdays, we always get cards from them.

SPuck:
I wouldn't call it weird, unless you think she is using the "grand puppy" as some kind of game to get grand children.

Curly Wurly Doggie Breath:
I need a pic of said Puppy :D

Secret:
Before hubby and I had kids, my mom called my dog her granddog. We thought nothing of it. She never spoke to her on the phone, but she always asked, "How's my granddog doing?" when we'd talk on the phone. I don't think it is that odd. (or maybe I"m that odd!)

Also, I need a photo of this puppy to better judge as well.

Zilla:
Another vote for not weird. My mom talks to my pup on the phone as well. Sometimes a pet will steal your heart unexpectedly and that's what it sounds like with mil. ;D